The Sum Of First 45 Natural Numbers Is:

1.	The Sum Of First 45 Natural Numbers Is:
Answer» Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, N = 45. Sn = n[2A + (n - 1)d] = 45x [2 x 1 + (45 - 1) x 1]/2 =45x 46/2 = (45 x 23)/2 = 45 x (20 + 3) = 45 x 20 + 45 x 3 = 900 + 135 = 1035. Shortcut Method: Sn = n(n + 1)/2=45(45 + 1)/2= 1035. Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45. Sn = n[2a + (n - 1)d] = 45x [2 x 1 + (45 - 1) x 1]/2 =45x 46/2 = (45 x 23)/2 = 45 x (20 + 3) = 45 x 20 + 45 x 3 = 900 + 135 = 1035. Shortcut Method: Sn = n(n + 1)/2=45(45 + 1)/2= 1035.

Answer»

Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, N = 45.

Sn = n[2A + (n - 1)d] = 45x [2 x 1 + (45 - 1) x 1]/2 =45x 46/2 = (45 x 23)/2

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shortcut Method:

Sn = n(n + 1)/2=45(45 + 1)/2= 1035.

Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.